|
Math 7326
Dynamical Systems
Fall 2019
Instructor: Vaughn
Climenhaga
- Office: 665 PGH
- Office hours: Wednesday 9-9:50am, Friday
1-1:50pm, or by appointment
- Email: climenha [at] math.uh.edu
Course information:
- Lectures: MWF, 12-12:50pm, AH 202
- Textbook: None required, though
at certain points we will follow proofs in
"One-Dimensional Dynamics" by de Melo and van
Strien, which is out of print but available
online at the second
author's website.
- Syllabus
This course will introduce the qualitative study of
dynamical systems via historically and
scientifically important examples such as the
three-body problem, nonlinear oscillators, the
Lorenz system, and the logistic map.
These examples illustrate how systems evolving in
time according simple deterministic rules can
exhibit complicated "chaotic" behavior. Each
of these systems depends on one or more parameters,
and a central part of the course will be to study
how the qualitative behavior of the system changes
(or does not change) as the parameters vary.
This will lead us to discuss topics such as KAM
theory, phase locking, bifurcations, period-doubling
cascades, renormalization, and parameter exclusion.
The topics to be covered in this course are largely
distinct from the topics covered in previous edition
of Math 7326 that I taught in Spring 2017, so
students who took that class would benefit from
taking this one as well. |
|
Cobweb diagrams for
the logistic map
|
